Iterated Block Gibbs Sampler for Ultrahigh-Dimensional Variable Selection and Model Averaging

Variable selection for generalized linear models and the Cox proportional-hazards model in ultrahigh dimensions via the iterated block Gibbs sampler (IBGS). The sampler is implemented in C with parallel block screening through 'OpenMP', and supports the gaussian, binomial and poisson families (fitted by least squares or iteratively reweighted least squares) as well as the Cox model for survival analysis (fitted by its Efron partial likelihood), together with the AIC, BIC, AICc and extended BIC model selection criteria.

IBGS

Iterated Block Gibbs Sampler for ultrahigh-dimensional variable selection and model averaging

IBGS performs variable selection for generalized linear models and the Cox proportional-hazards model when the number of predictors is very large. The sampler is implemented in C with parallel block screening through OpenMP, and returns a small set of high-scoring models together with marginal inclusion probabilities and model-averaged predictions. Methods are described in Chen (2022).

Features

• Families: gaussian, binomial and poisson GLMs (least squares / IRLS), the Cox model for survival data (Efron partial likelihood), and linear mixed models.
• Selection criteria: AIC, BIC, AICc and extended BIC (exBIC).
• Two samplers per family: an iterated block Gibbs sampler with screen–select–threshold refinement (*IBGS), and a plain block Gibbs sampler (*Gibbs).
• Model averaging built in: predict(), fitted() and coef() average over the retained top models with smooth-SIC (BMA-style) weights.
• Diagnostics: a trace of the criterion sequence, marginal inclusion probabilities, and top-model visit frequencies.
• Convergence diagnostics: the Gelman–Rubin shrink-factor evolution, the Geweke z-statistic, the effective sample size, and the autocorrelation of the criterion trace.
• Scales to large p: the per-generation indicator matrix is summarized in C, so the fitted object stays compact even for thousands of predictors.

Installation

Install the released version from CRAN:

install.packages("IBGS")

A C compiler is required to build from source (OpenMP is used when available for the parallel block screening). To install the development version from a local copy of the source:

R CMD INSTALL IBGS

or, from within R:

# install.packages("remotes")
remotes::install_local("IBGS")

Quick start

library(IBGS)

## 50 predictors, only the first three are active
x <- matrix(rnorm(100 * 50), 100, 50)
y <- rowSums(x[, 1:3]) + rnorm(100)

fit <- glmIBGS(y, x, criterion = "BIC")
fit                       # concise overview
summary(fit)              # selected-variable, top-model tables and convergence diagnostics
plot(fit)                 # criterion trace, marginal probabilities, model frequencies, R_hat, autocorrelation

coef(fit)                 # best model; coef(fit, average = TRUE) to average
predict(fit, x[1:5, ])    # model-averaged predictions on new data
fitted(fit)               # model-averaged fitted values

Functions

Each sampler returns an object of class "IBGS" with print(), summary(), plot(), coef(), predict() and fitted() methods. The plotting helpers plotICtrace(), plotMargProb(), plotModelFreq(), plotGelman() and plotAutocorr() are also exported for drawing the individual diagnostics.

Common arguments include criterion (selection criterion), n.models (number of top models to retain and average over), threshold (marginal-probability cut-off for the reported selected variables), inv.temp (inverse temperature), and n.cores (OpenMP threads for block screening). For survival data, coxIBGS(y, status, x) takes the follow-up time y and the event indicator status; for lmeIBGS(), group/Z specify the random-effects structure.

Documentation

See the package help (?glmIBGS, ?coxIBGS, ?predict.IBGS, ...) and the package vignette:

vignette("IBGS")

Reference

Chen, L. (2022). Model selection and averaging by Gibbs sampler with a tropical cyclone seasonal forecasting application, PhD thesis, The University of Melbourne. https://hdl.handle.net/11343/311691

License

GPL-3.